A Three-Dimensional Numerical Model of an Active Cell Cortex in the Viscous Limit

The cell cortex is a highly dynamic network of cytoskeletal filaments in which motor proteins induce active cortical stresses which in turn drive dynamic cellular processes such as cell motility, furrow formation or cytokinesis during cell division. Here, we develop a three-dimensional computational model of a cell cortex in the viscous limit including active cortical flows. Combining active gel and thin shell theory, we base our computational tool directly on the force balance equations for the velocity field on a discretized and arbitrarily deforming cortex. Since our method is based on the general force balance equations, it can easily be extended to more complex biological dependencies in terms of the constitutive laws or a dynamic coupling to a suspending fluid. We validate our algorithm by investigating the formation of a cleavage furrow on a biological cell immersed in a passive outer fluid, where we successfully compare our results to axi-symmetric simulations. We then apply our fully three-dimensional algorithm to fold formation and to study furrow formation under the influence of non-axisymmetric disturbances such as external shear. We report a reorientation mechanism by which the cell autonomously realigns its axis perpendicular to the furrow plane thus contributing to the robustness of cell division under realistic environmental conditions.

Design Calculations of the Limiting Characteristics of Heat Pipes for Cooling Active Phased Antenna Arrays

The article provides an algorithm for calculating the limiting characteristics of heat pipes for cooling active phased antenna arrays at a given saturation temperature. The maximum transmitted power is determined taking into account the limitations of the heat pipes operation by the capillary limit, by boiling (transition to film boiling, boiling limit), by the sonic limit at which the speed of steam reaches the speed of sound (sonic limit), by the entrainment of droplets liquid coolant from the surface of the wick with a counter flow of steam (entertainment limit) and viscous limit, which is realized at low temperatures (viscous limit). It is shown that an increase in the thickness of the wick and its porosity may be necessary to increase the capillary limit of heat pipes, while an increase in the thickness of the wick increases the thermal resistance of the tube and, accordingly, can lead to overheating of the cooled elements. Based on the above algorithm, design calculations for two types of heat pipes have been carried out. The dependences of various limits of the heat pipe on the operating temperature are plotted. Based on the above algorithm, calculations were performed for two types of heat pipes.

The Inviscid Limits to Piecewise Smooth Solutions for a General Parabolic System

We study the viscous limit problem for a general system of conservation laws. We prove that if the solution of the underlying inviscid problem is piecewise smooth with finitely many noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding viscous system which converge to the inviscid solutions away from shock discontinuities at a rate of ε1 as the viscosity coefficient ε vanishes.